Final answer:
The cash payment that Patrick will receive during the liquidation of Oliver, Patrick & Quincy LLP is $6,000.
Step-by-step explanation:
To calculate the cash payment that Patrick receives during the liquidation of Oliver, Patrick & Quincy LLP, we need to determine the amount of capital each partner will receive. The income-sharing ratio of 5:1:4 means that Oliver, Patrick, and Quincy will receive 5/10, 1/10, and 4/10 of the total capital, respectively.
The total capital available is the partners' capital account balances plus the amount realized from the noncash assets. Therefore, the total capital is $40,000 + $120,000 = $160,000.
Patrick's share is 1/10 of $160,000, which is $16,000. However, Patrick also has a $10,000 loan payable to him, so the final cash payment that Patrick will receive is $16,000 - $10,000 = $6,000.